It is eight-and-a-half years since Jermain Defoe left West Ham United but the club's fans will never forget. The Tottenham Hotspur striker's every touch here was jeered and the abusive choruses from the away enclosure left him in no doubt as to where his stock stands in the East End. His response on the field, though, was articulate and emphatic.

Tottenham had lost their momentum from early in the first-half when Defoe received possession on halfway, wriggled away from challengers, jinked and sizzled a shot past Jussi Jaaskelainen. His ninth goal of the season for Tottenham was all his own work, it was simply outstanding and it would have filled him with satisfaction, although he resisted the temptation to make the point to his tormentors.

Defoe's second of the afternoon was the consummate team goal, resulting from a decisive burst from Aaron Lennon and it moved Tottenham towards a vital result, which eased their recent nerves in the Premier League. Gareth Bale, who also enjoyed an excellent game, scored their other one and a landmark goal for Andy Carroll, his first in nine appearances for West Ham, did not threaten to affect the outcome, despite it provoking a late rally from his team.

Sam Allardyce, the West Ham manager, was left to lament a "poor performance," riddled with uncharacteristic "defensive fragilities" but André Villas-Boas's enjoyment was rather more pronounced. He pulled Defoe close when he substituted him late on and the striker could revel in public praise.

"Jermain's first goal was decisive because it unlocked the game," Villas-Boas said. "He's an incredible striker, his form is absolutely immense. His hunger for goals is exactly what you want. I couldn't ask for any more."

It was one of those occasions when everything came off for Villas-Boas and some people, even him, might suggest that it was about time. "We have been chasing this for some time – a solid 90-minute performance," he said. His decision to drop William Gallas for Michael Dawson was vindicated; Clint Dempsey had a fine game and Mousa Dembélé's confinement to a late substitute's cameo because of his on-going hip trouble was not problematic.

Tottenham were the better team from the first whistle, with Allardyce unable to explain what had gone wrong. "It looked like we were overawed and I don't know why," he said. "There is not a lot I can do to defend the players, even though I'd like to."

Tottenham's bright start had featured Defoe looking lively and Bale hitting the underside of the crossbar from distance, following a blistering burst. The winger had also been cut down from behind by Joey O'Brien, who was fortunate to escape with a yellow card, and the game featured niggle, not least between the benches.

Tottenham's fitness coach José Mário Rocha clashed with the West Ham assistant Neil McDonald, and the fourth official, Mark Clattenburg, had to step in to restore calm. It was Clattenburg's first assignment since the Stamford Bridge controversy, when he was accused of directing inappropriate language towards the Chelsea midfielder Mikel John Obi. Clattenburg was cleared of any wrongdoing by the Football Association and there was a feeling, articulated by both managers, that it was good to see him back.

Defoe had endured a frustrated lull and he was booked for catching Winston Reid. But he sparked in breathtaking fashion just before half-time when he held the ball up on the right flank, under heavy pressure, before spinning back inside between Reid and George McCartney. Running at Mark Noble, he cut inside him to make room for the right-footed shot and, from outside the area, it curled and fizzed past Jaaskelainen.

The second half brought thrills, as West Ham emerged with greater purpose. The substitute Matt Jarvis drew a smart save from Hugo Lloris and he was also thwarted by the French goalkeeper when West Ham broke and Kevin Nolan crossed. The atmosphere was pulsating, although some of the chants from the West Ham corner were deeply unsavoury.

It was Tottenham who pulled clear, Bale forced Jaaskelainen into a good save and Dempsey rattled the crossbar before the pressure told, Bale taking Dempsey's cute chip and getting over his shot to force it into the far corner. Defoe's second made the points safe for Tottenham. After Nolan had been robbed in midfield, Tottenham sprang, with Dempsey touching through for Lennon, who beat James Tomkins to streak clear. Lennon squared unselfishly for Defoe, and he rolled into the empty net.

Carroll's goal came after O'Brien seized upon Steven Caulker's loose clearance and his header looped into the far corner. It might not have the game's final goal, as West Ham had a couple of scrambled efforts and both Defoe and Bale went close.

For West Ham, the fixtures do not get any easier. Tottenham can savour a tonic. Man of the match Jermain Defoe (Tottenham Hotspur)